Don't have
experience with this, but they must have some natural predator, and if you can find some way to leave some around long
enough, that predator will show up--that's what Paul just said in the podcast I'm listening to (review of
Gaia's Garden chapter 7, podcast 075.)
Diatomaceous earth could help in the immediate and be safe for the ecosystem...but even that will probably kill some beneficial bugs as well as the ones you don't want.
Do you have a lot of currants all growing together? could you let some diversity grow in in the middle of the area, to make a bit of an edge/border through the middle of that section?
From my web search, it looks like current conventional opinion is that there are few natural predators...so if you do observe something eating them you're doing some new research.
Some other things you might try if you have them:
chickens
ducks
geese
guinea fowl
bird bath (to attract birds that might like to eat them?)
This information brought to you by my butt. May not be true in any way.